"We anticipated bigger offers in free agency, but Aaron wanted to stay with the Packers," Rosenhaus said.
The Packers opted against using their franchise tag on Jones before last week's deadline. Instead, the franchise continued its talks with Jones on a long-term contract.
On Sunday, Jones confirmed his return to the Packers with a tweet that read: "Let's run it back."
The Packers selected Jones in the fifth round of the 2017 draft out of UTEP. He ranked fourth in the league last season with 1,104 rushing yards despite sitting out two games because of a calf injury. It was his second consecutive 1,000-yard rushing season.
Jones was named to his first Pro Bowl in the 2020 season. The year before, he ran for 1,084 yards and led the NFL with 19 touchdowns.
Green Bay drafted former Boston College running back A.J. Dillon in the second round last year in case Jones or Jamaal Williams left in free agency.